



'''simple docstring'''






def  lowerCamelCase__			(		_A							):

  # bit count represents no. of bits in the gray code
  if bit_count < 0:
    raise ValueError('The given input must be positive'							)

  # get the generated string sequence
  a		:   Optional[Any]	  =	gray_code_sequence_string(_A							)
  #
  # convert them to integers
  for i in range(len(_A							)							):
    a		:   Union[str, Any]	  =	int(sequence[i]					,     2							)

  return sequence
def  lowerCamelCase__			(		_A							):

  # The approach is a recursive one
  # Base case achieved when either n = 0 or n=1
  if bit_count == 0:
    return ["0"]

  if bit_count == 1:
    return ["0", "1"]

  a		:   Dict	  =	1 << bit_count  # defines the length of the sequence
  # 1<< n is equivalent to 2^n

  # recursive answer will generate answer for n-1 bits
  a		:   Dict	  =	gray_code_sequence_string(bit_count - 1							)

  a		:   int	  =	[]

  # append 0 to first half of the smaller sequence generated
  for i in range(seq_len // 2							):
    a		:   Dict	  =	'0' + smaller_sequence[i]
    sequence.append(_A							)

  # append 1 to second half ... start from the end of the list
  for i in reversed(range(seq_len // 2							)							):
    a		:   int	  =	'1' + smaller_sequence[i]
    sequence.append(_A							)

  return sequence


if __name__ == "__main__":
     import doctest

     doctest.testmod()




'''simple docstring'''






def  lowerCamelCase__			(		_A					,     _A					,     _A=False							):

  if isinstance(_A					,     _A							) and isinstance(_A					,     _A							):
    a		:   Tuple	  =	len(set_a.intersection(_A							)							)

    if alternative_union:
      a		:   Union[str, Any]	  =	len(_A							) + len(_A							)
    else:
      a		:   Optional[Any]	  =	len(set_a.union(_A							)							)

    return intersection / union

  if isinstance(_A					,     (list, tuple)							) and isinstance(_A					,     (list, tuple)							):
    a		:   int	  =	[element for element in set_a if element in set_b]

    if alternative_union:
      a		:   Optional[int]	  =	len(_A							) + len(_A							)
      return len(_A							) / union
    else:
      a		:   Tuple	  =	set_a + [element for element in set_b if element not in set_a]
      return len(_A							) / len(_A							)

    return len(_A							) / len(_A							)
  return None


if __name__ == "__main__":
     lowerCAmelCase:   str					=		{'a', 'b', 'c', 'd', 'e'}
     lowerCAmelCase:   Optional[Any]					=		{'c', 'd', 'e', 'f', 'h', 'i'}
     print(jaccard_similarity(set_a, set_b))